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# Problem set 3 (Business statistics)

 “In sample we deal with …, in populations with…” 1.) Statistics2.) parameters Which of the following provides a measure of central location for the data?a.) Standard deviation b.) Meanc.) Varianced.) Range Mean A numerical value used as a summery measure for a sample, such as sample mean, is known as Sample Statistics Since the population size is always larger than the sample size, then the sample statistic can be smaller, larger, or equal to the population parameter μ is an example of population parameter The median of a sample will always equal the 50th percentile The median is a measure of central location The 75th percentile is referred as the Third quartile The pth quertial is a value such that at least p percent of the observation are less than equal to this value The difference between the largest and the smallest data values is the range The first quartile Is the same as the 25th percentile Which of the following is not a measure of central location?a.)Mean b.) Medianc.) Varianced.) Mode Variance If a data set has an even number of observation, the median is the average value of the two middle item when all item are arranged in ascending order Which of the following is a measure of dispersiona.) Percentiles b.) Quartilesc.) Interquartile range d.) all of the above interquartile range the most frequent occurring value of a data set is called the mode The interquartile range is the difference between the third quartile and the first quartile If index i (which is used to determine the location of the pth percentile) is not an integer, its value should be rounded up When the data are skewed to the right, the measure of skewness will be positive when data are positively skewed , the mean will usually be greater than the median Which of the following is not a measure of dispersiona.) the rangeb.) the 50th percentialc.) the standard deviationd.) the interquartile range the 50th percentile The range is used as a measure of variability to overcome what difficulty of the range? the range influenced too much by extreme values If the variance of a data set is correctly computed with the formula using n-1 in the denominator the data set is a sample In computing descriptive statistics from grouped data ( like frequency histogram) data values are treated as if they occur at the midpoint of a class The measure of dispersion that is influenced most by extreme values is the range When should measure of location and dispersion be computed from grouped data rather than from individual data values? only when individuals data values are unavaliable The descriptive measure of dispersion that is based on the concept of a deviation about the mean is the standard deviation The measure of location which is the most likely to be influenced by extreme values in the data set is the mean The most important statistical descriptive measure of the location of data set is the mean The numerical value of the standard deviation can never be negative The sample variance could be smaller, equal to, or larger than the true value of the population variance The variance can never be negative the sum of deviations of the individual data elements from their mean is always equal to zero Standard deviation of the population σ mean of the population μ variance of the population σ^2 size of the population N mean of the sample -X size of sample N a numerical measure of linear associate between two variables correlation coefficient of covariance positive values of covariance indicates positive relation between the independent and the dependent variables the coefficient of correlation ranges between -1 and +1 the coefficient of correlation cannot be larger than 1 When the smallest and largest percentage of item are removed from data set and the mean is computed, the mean of the remaining data is the trimmed mean during a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). the variance of temp of the 10 days period must be at least 0 which of the following is not a measure of dispersiona.) modeb.) Standard deviation c.) ranged.) interquartile range mode